Due to concerns about the underinflation of footballs, the National Football League (NFL) created a series of standards that must be met for the weight, length, and the long and short circumferences of each ball. It is stated that the balls are to be inflated to between 12.5 to 13.5 pounds. The pressure output by the ball pump is approximately Normal with a mean of 13 pounds and a standard deviation of 0.25 pounds. At each game, the home team must supply 12 balls to the referee 2 hours and 15 minutes prior to the start of the game for inspection.

(a) What is the probability that a randomly selected ball will not meet the inflation specifications?

Based on the weight requirement that the ball should be inflated to, the probability that a random ball will not meet this specification is 0.0456.

What is the probability a ball will not meet inflation specifications?

The balls are to be inflated to reach between 12.5 to 13.5 pounds.

The probability they won't meet this specification is:

= 1 - ( P (Z₁₃.₅) - P (Z₁₂.₅) )

Z₁₃.₅ = (13.5 - 13) / 0.25

= 2

Z₁₂.₅ = (12.5 - 13) / 0.25

= -2

From the Z table, P (Z₁₃.₅) is therefore 0.9772 and P (Z₁₂.₅) is 0.0228.

The probability that the inflation requirement is not met is:

= 1 - (0.9772 - 0.0228)

= 0.0456

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